Abstract
The first paper [10] (whose results were announced in [8]) developed the necessary ‘algebra of cubes’. Categories G of ω-groupoids and C of crossed complexes were defined, and the principal result of [10] was an equivalence of categories γ : G → C. Also established were a version of the homotopy addition lemma, and properties of ‘thin’ elements, in an ω-groupoid. In particular it was proved that an ω-groupoid is a special kind of Kan cubical complex, in that every box has a unique thin filler. All these results will be used here.
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